This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion equations.We apply the Fourier analysis techniq...This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion equations.We apply the Fourier analysis technique to symbolically compute eigenvalues and eigenvectors of the amplification matrices for both DDG methods with different coefficient settings in the numerical fluxes.Based on the eigen-structure analysis,we carry out error estimates of the DDG solutions,which can be decomposed into three parts:(i)dissipation errors of the physically relevant eigenvalue,which grow linearly with the time and are of order 2k for P^(k)(k=2,3)approximations;(ii)projection error from a special projection of the exact solution,which is decreasing over the time and is related to the eigenvector corresponding to the physically relevant eigenvalue;(iii)dissipative errors of non-physically relevant eigenvalues,which decay exponentially with respect to the spatial mesh sizeΔx.We observe that the errors are sensitive to the choice of the numerical flux coefficient for even degree P^(2)approximations,but are not for odd degree P^(3)approximations.Numerical experiments are provided to verify the theoretical results.展开更多
The impedance matching of absorbers is a vital factor affecting their microwave absorption(MA)properties.In this work,we controllably synthesized Material of Institute Lavoisier 88C(MIL-88C)with varying aspect ratios(...The impedance matching of absorbers is a vital factor affecting their microwave absorption(MA)properties.In this work,we controllably synthesized Material of Institute Lavoisier 88C(MIL-88C)with varying aspect ratios(AR)as a precursor by regulating oil bath conditions,followed by one-step thermal decomposition to obtain carbon-coated iron-based composites.Modifying the precursor MIL-88C(Fe)preparation conditions,such as the molar ratio between metal ions and organic ligands(M/O),oil bath temperature,and oil bath time,influenced the phases,graphitization degree,and AR of the derivatives,enabling low filler loading,achieving well-matched impedance,and ensuring outstanding MA properties.The MOF-derivatives 2(MD_(2))/polyvinylidene Difluoride(PVDF),MD_(3)/PVDF,and MD4/PVDF absorbers all exhibited excellent MA properties with optimal filler loadings below 20 wt%and as low as 5 wt%.The MD_(2)/PVDF(5 wt%)achieved a maximum effective absorption bandwidth(EAB)of 5.52 GHz(1.90 mm).The MD_(3)/PVDF(10 wt%)possessed a minimum reflection loss(RL_(min))value of−67.4 at 12.56 GHz(2.13 mm).A symmetric gradient honeycomb structure(SGHS)was constructed utilizing the high-frequency structure simulator(HFSS)to further extend the EAB,achieving an EAB of 14.6 GHz and a RL_(min) of−59.0 dB.This research offers a viable inspiration to creating structures or materials with high-efficiency MA properties.展开更多
In this paper,a generalized form of the symmetric Banzhaf value for cooperative fuzzy games with a coalition structure is proposed.Three axiomatic systems of the symmetric Banzhaf value are given by extending crisp ca...In this paper,a generalized form of the symmetric Banzhaf value for cooperative fuzzy games with a coalition structure is proposed.Three axiomatic systems of the symmetric Banzhaf value are given by extending crisp case.Furthermore,we study the symmetric Banzhaf values for two special kinds of fuzzy games,which are called fuzzy games with multilinear extension form and a coalition structure,and fuzzy games with Choquet integral form and a coalition structure,respectively.展开更多
The reduction approaches are presented for vibration control of symmetric, cyclic periodic and linking structures. The condensation of generalized coordinates, the locations of sensors and actuators, and the relation ...The reduction approaches are presented for vibration control of symmetric, cyclic periodic and linking structures. The condensation of generalized coordinates, the locations of sensors and actuators, and the relation between system inputs and control forces are assumed to be set in a symmetric way so that the control system posses the same repetition as the structure considered. By employing proper transformations of condensed generalized coordinates and the system inputs, the vibration control of an entire system can be implemented by carrying out the control of a number of sub-structures, and thus the dimension of the control problem can be significantly reduced.展开更多
Irreversible drift-diffusion processes are very common in biochemical reactions.They have a non-equilibrium stationary state(invariant measure)which does not satisfy detailed balance.For the corresponding Fokker-Planc...Irreversible drift-diffusion processes are very common in biochemical reactions.They have a non-equilibrium stationary state(invariant measure)which does not satisfy detailed balance.For the corresponding Fokker-Planck equation on a closed manifold,using Voronoi tessellation,we propose two upwind finite volume schemes with or without the information of the invariant measure.Both schemes possess stochastic Q-matrix structures and can be decomposed as a gradient flow part and a Hamiltonian flow part,enabling us to prove unconditional stability,ergodicity and error estimates.Based on the two upwind schemes,several numerical examples–including sampling accelerated by a mixture flow,image transformations and simulations for stochastic model of chaotic system–are conducted.These two structurepreserving schemes also give a natural random walk approximation for a generic irreversible drift-diffusion process on a manifold.This makes them suitable for adapting to manifold-related computations that arise from high-dimensional molecular dynamics simulations.展开更多
Symmetric spaces of Cayley type are a higher dimensional analogue of a onesheeted hyperboloid in R3. They form an important class of causal symmetric spaces. To a symmetric space of Cayley type M, one can associate a ...Symmetric spaces of Cayley type are a higher dimensional analogue of a onesheeted hyperboloid in R3. They form an important class of causal symmetric spaces. To a symmetric space of Cayley type M, one can associate a bounded symmetric domain of tube type D. We determine the full causal automorphism group of M. This clarifies the relation between the causal automorphism group and the holomorphic automorphism group of D.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.11871428 and 12071214)the Natural Science Foundation for Colleges and Universities of Jiangsu Province of China(Grant No.20KJB110011)+1 种基金supported by the National Science Foundation(Grant No.DMS-1620335)and the Simons Foundation(Grant No.637716)supported by the National Natural Science Foundation of China(Grant Nos.11871428 and 12272347).
文摘This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion equations.We apply the Fourier analysis technique to symbolically compute eigenvalues and eigenvectors of the amplification matrices for both DDG methods with different coefficient settings in the numerical fluxes.Based on the eigen-structure analysis,we carry out error estimates of the DDG solutions,which can be decomposed into three parts:(i)dissipation errors of the physically relevant eigenvalue,which grow linearly with the time and are of order 2k for P^(k)(k=2,3)approximations;(ii)projection error from a special projection of the exact solution,which is decreasing over the time and is related to the eigenvector corresponding to the physically relevant eigenvalue;(iii)dissipative errors of non-physically relevant eigenvalues,which decay exponentially with respect to the spatial mesh sizeΔx.We observe that the errors are sensitive to the choice of the numerical flux coefficient for even degree P^(2)approximations,but are not for odd degree P^(3)approximations.Numerical experiments are provided to verify the theoretical results.
基金financially supported by the National Natural Science Foundation of China(51972049,52073010,and 52373259)the Projects of the Science and Technology Department of Jilin Province(20230201132GX)the Projects of the Education Department of Jilin Province(JJKH20220123KJ)。
文摘The impedance matching of absorbers is a vital factor affecting their microwave absorption(MA)properties.In this work,we controllably synthesized Material of Institute Lavoisier 88C(MIL-88C)with varying aspect ratios(AR)as a precursor by regulating oil bath conditions,followed by one-step thermal decomposition to obtain carbon-coated iron-based composites.Modifying the precursor MIL-88C(Fe)preparation conditions,such as the molar ratio between metal ions and organic ligands(M/O),oil bath temperature,and oil bath time,influenced the phases,graphitization degree,and AR of the derivatives,enabling low filler loading,achieving well-matched impedance,and ensuring outstanding MA properties.The MOF-derivatives 2(MD_(2))/polyvinylidene Difluoride(PVDF),MD_(3)/PVDF,and MD4/PVDF absorbers all exhibited excellent MA properties with optimal filler loadings below 20 wt%and as low as 5 wt%.The MD_(2)/PVDF(5 wt%)achieved a maximum effective absorption bandwidth(EAB)of 5.52 GHz(1.90 mm).The MD_(3)/PVDF(10 wt%)possessed a minimum reflection loss(RL_(min))value of−67.4 at 12.56 GHz(2.13 mm).A symmetric gradient honeycomb structure(SGHS)was constructed utilizing the high-frequency structure simulator(HFSS)to further extend the EAB,achieving an EAB of 14.6 GHz and a RL_(min) of−59.0 dB.This research offers a viable inspiration to creating structures or materials with high-efficiency MA properties.
基金supported by Natural Science Foundation Youth Project of China (No. 71201089)National Natural Science Foundation of China (Nos. 71071018 and 71271217)Natural Science Foundation Youth Project of Shandong Province,China(No. ZR2012GQ005)
文摘In this paper,a generalized form of the symmetric Banzhaf value for cooperative fuzzy games with a coalition structure is proposed.Three axiomatic systems of the symmetric Banzhaf value are given by extending crisp case.Furthermore,we study the symmetric Banzhaf values for two special kinds of fuzzy games,which are called fuzzy games with multilinear extension form and a coalition structure,and fuzzy games with Choquet integral form and a coalition structure,respectively.
基金Project supported by the National Natural Science Foundation of China (No.60034010) the Australia Research Council Discovery-Projects Grant (No.DP0210716)
文摘The reduction approaches are presented for vibration control of symmetric, cyclic periodic and linking structures. The condensation of generalized coordinates, the locations of sensors and actuators, and the relation between system inputs and control forces are assumed to be set in a symmetric way so that the control system posses the same repetition as the structure considered. By employing proper transformations of condensed generalized coordinates and the system inputs, the vibration control of an entire system can be implemented by carrying out the control of a number of sub-structures, and thus the dimension of the control problem can be significantly reduced.
基金Jian-Guo Liu was supported in part by NSF under awards DMS-2106988by NSF RTG grant DMS-2038056Yuan Gao was supported by NSF under awards DMS-2204288.
文摘Irreversible drift-diffusion processes are very common in biochemical reactions.They have a non-equilibrium stationary state(invariant measure)which does not satisfy detailed balance.For the corresponding Fokker-Planck equation on a closed manifold,using Voronoi tessellation,we propose two upwind finite volume schemes with or without the information of the invariant measure.Both schemes possess stochastic Q-matrix structures and can be decomposed as a gradient flow part and a Hamiltonian flow part,enabling us to prove unconditional stability,ergodicity and error estimates.Based on the two upwind schemes,several numerical examples–including sampling accelerated by a mixture flow,image transformations and simulations for stochastic model of chaotic system–are conducted.These two structurepreserving schemes also give a natural random walk approximation for a generic irreversible drift-diffusion process on a manifold.This makes them suitable for adapting to manifold-related computations that arise from high-dimensional molecular dynamics simulations.
文摘Symmetric spaces of Cayley type are a higher dimensional analogue of a onesheeted hyperboloid in R3. They form an important class of causal symmetric spaces. To a symmetric space of Cayley type M, one can associate a bounded symmetric domain of tube type D. We determine the full causal automorphism group of M. This clarifies the relation between the causal automorphism group and the holomorphic automorphism group of D.
